Uncertainty in MRIO-based GHG footprints

15. Input-Output-Workshop Osnabrück

Simon Schulte*, Arthur Jakobs, Stefan Pauliuk

2024-03-01

Model uncertainty matters…

  • … for robust decision-making
  • … to guide GMRIO compilers to “uncertainty hot-spots” to allocate resources more efficiently

Uncertainty in EE-MRIO: Current state

  • database comparisons: Satellite accounts are largest source of discrepancy

https://robbieandrew.github.io/consumption/index.html

https://robbieandrew.github.io/consumption/index.html

Uncertainty in EE-MRIO: Current state

  • database comparisons: Satellite accounts are largest source of discrepancy
  • mostly points estimates, and, if at all, qualitative considerations of uncertainty
  • few studies provide quantitative estimation of parametric uncertainties [1–8]
  • two GMRIO databases that publish uncertainty estimates alongside each data entry (except for GHG extensions): Eora [9] & GLORIA [10]
  • all studies use Monte-Carlo (MC) simulations to propagate uncertainty from model input parameters to model outputs

Aim and scope of our study

  • estimate the parametric uncertainty of the GHG satellite accounts
  • estimate how the uncertainty propagates to GHG footprints
  • overcome two shortcomings from previous approaches:
    • #1: Uncertainty of the raw input data based on simplistic assumptions
    • #2: Correlations between variables obtained by disaggregating a common input data point are ignored
  • Scope:
    • Year 2015
    • GHGs CO\(_2\), CH\(_4\), N\(_2\)O
    • EXIOBASE country/sector resolution

Compiling GHG accounts

Statistical concept

Our workflow

Our workflow

Our workflow

Our workflow

Overcoming shortcomings of previous approaches

#1: Uncertainty of the raw input data based on simplistic assumptions

Two common approaches

Heuristics:

[2]

Statistical model: [1]

Our approach

UNFCCC National Inventory Reports (only in .pdf format 😭)

But now, as .csv on Zenodo: https://zenodo.org/records/10037714 😁

#2: A disregard of correlations between variables obtained by disaggregating a common input data point

Data disaggregation: Residence adjustment

Data disaggregation: Assign to MRIO sectors

Uncertainty propagation involving data disaggregation

G parallelogram1 Y₀ parallelogram2 Y₁ parallelogram1->parallelogram2 parallelogram3 Y₂ parallelogram1->parallelogram3 parallelogram4 Y₃ parallelogram1->parallelogram4

where \(\sum Y_i = Y_0\).

Uncertainty propagation involving data disaggregation

G parallelogram1 Y₀ parallelogram2 Y₁=α₁Y₀ parallelogram1->parallelogram2 parallelogram3 Y₂=α₂Y₀ parallelogram1->parallelogram3 parallelogram4 Y₃=α₃Y₀ parallelogram1->parallelogram4

where \(\sum \alpha_i = 1\).

Constraints & Information

G parallelogram1 Y₀ parallelogram2 Y₁=α₁Y₀ parallelogram1->parallelogram2 parallelogram3 Y₂=α₂Y₀ parallelogram1->parallelogram3 parallelogram4 Y₃=α₃Y₀ parallelogram1->parallelogram4
  1. Mean \(\mu\) and Standard Deviation \(\sigma\) of aggregate data (UNFCCC/EDGAR)
  2. Mean sector shares for disaggregate data \(\boldsymbol{\alpha}\) (proxy data: SUT/PEFA/…)
  3. sum-to-one constraint: \(\sum \alpha_i = 1\)
  4. no negative emissions

Sampling procedure

Step 1: Sample aggregate data from truncated normal distribution: \(y_0 \sim tN(\mu,\sigma,a = 0)\)

Step 2: Sample sector shares from Dirichlet distribution: \(x_1, x_2, ..., x_K \sim Dir(\boldsymbol\alpha,\gamma = \hat\gamma)\)

Step 3: Multiply both \(y_i = x_i y_0\ \forall\ i\in{1,..,K}\)

Sampling from a Dirichlet distribution

Sampling from a Dirichlet distribution

The \(\gamma\) parameter

\(\require{colorx} x_1, x_2, ..., x_K \sim Dir(\boldsymbol\alpha,\color{red} \gamma\color{black})\)

The \(\gamma\) parameter

\(\require{colorx} x_1, x_2, ..., x_K \sim Dir(\boldsymbol\alpha,\color{red}{\gamma=\hat\gamma} \color{black})\)

Maximum Entropy (MaxEnt) principle:
The least informative probability distribution consistent with a given set of constraints is the one which maximizes the entropy [11]

Finding \(\hat\gamma\) which maximises the entropy

\(\require{colorx} x_1, x_2, ..., x_K \sim Dir(\boldsymbol\alpha,\color{red}{\gamma=\hat\gamma} \color{black})\)

\[ \max_{\gamma>0}\ h(\gamma) = ln B(\gamma\boldsymbol\alpha) + (\gamma\alpha_0-K)\psi(\gamma\alpha_0) - \sum_{i=1}^K (\gamma\alpha_i-1)\psi(\gamma\alpha_i), \] where

  • \(\psi(x)\) is the Digamma function \(\psi(x) = \frac{d}{dn}ln(\Gamma(x)) = \frac{\Gamma'(x)}{\Gamma(x)}\),
  • \(\Gamma(x)\) is the Gamma function: \(\Gamma(x) = \int_0^\infty t^{x-1}e^{-t}dt\),
  • \(B(\gamma\boldsymbol\alpha)\) is the multivariate beta function: \(B(\gamma\boldsymbol\alpha) = \frac{\prod_{i=1}^K \Gamma(\gamma\alpha_i)}{\Gamma(\sum_{i=1}^K \gamma\alpha_i)}\)

Correlations

Why correlations matter

Why correlations matter

Results: Country level

Results: Sector level

Results: Correlations

Conclusion

  • Uncertainty hot-spots:
    • National level:
      • CO\(_2\): small economies subject to large residence adjustments
      • In general larger uncertainties for CH\(_4\) and esp. N\(_2\)O
    • Sector level: Overall: high uncertainties (median CV of ~1)
  • Ignoring correlations would overestimate CO\(_2\)-footprints and underestimate N\(_2\)O-footprints

Thank you!

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